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From: Aatu Koskensilta on 19 Feb 2010 10:47
Marc Alcob� Garc�a <malcobe(a)gmail.com> writes:

> If ZFC is now regarded as a formalization of the metatheory, then
> Con(T) is a theorem in the metatheory for each T. So, for each T we
> have a model. I don't see why from this we cannot conclude in the
> metatheory that T' (i. e. ZFC) has a model...

In order to conclude that all finite subtheories of ZFC are consistent
from the fact that Con(T) is provable in ZFC for any finite subtheory T
of ZFC we need to appeal to the principle:

If it is provable in ZFC for every n that P(n) then P(n) for all n.

This principle is not provable in ZFC.

--
Aatu Koskensilta (aatu.koskensilta(a)uta.fi)

"Wovon man nicht sprechan kann, dar�ber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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